Nah... Destiny's only ever had 2 gamemode
Rumble
Clash, sometimes with special quests, objectives
Control
Clash with objectives
Rift
Clash with a ball
Trials
3v3 elimination clash
Salvage
See trials /w objective
Skirmish
3v3 clash
Supremacy
Clash with things to pick up
Countdown
See Salvage
Unfortunately since kills are often directly tied to the victory condition in Destiny... every mode is just Team Deathmatch. Except Zone Control.